One of the least populated states? Check. Proximity to nothing? Check. Biggest annual event is a motorcycle rally? Rural as all get out? Yes and yes. Usually when I do a piece like this, I talk about historic parks that aren't there any more. Stony Point at Lake Kampeska and Ruskin Park fit that bill here (I'm skipping them, but just know they've been gone a long time). But oddly, there's actually a lot in South Dakota; way way more than you'd expect for a state with less than a million residents and no culturally significant cities. Yeah, there's Fargo. You only know that there was a Coen Brothers movie named that though, don't play. There's also Mount Rushmore, which is kinda a big deal (don't forget the Crazy Horse sculpture that's being built down the street). South Dakota is, I suppose, kinda an attraction onto itself - part of the Great American Road Trip, a place of truly wild and where people can feel as though even in a very controlled environment, they are in the deepest of western frontiers.
To that end, the fantasy of the west is seen in multiple themed attractions: Cosmos Mystery Area is a classic Tilt House style attraction in the vein of what Gravity Falls was based around on Disney Channel. It's located on the drive into Mount Rushmore, ensuring a healthy group of bored kids yearning for stimulation screaming at their parents to pull over. Of course there's a bunch of pseudo-supernatural explanations about how their optical illusions work, but you already know "magic" in all forms is fake. 1880 Town in Midland attempts by comparison to traffic in the more "real". It's a living history museum showing frontier life with period buildings and artifacts that are well kept. Living history museums aren't necessarily unique; what is unique are the home made automated displays at the Chester & Hester's Dino-Rama version of 1880 Town known as 1880 Cowboy Town in Sioux Falls. Want to see someone's attempt at making Mr. Lincoln on a shoestring budget? Well, you can.
The fantasy of the American West contrasts with the realities of settler life, crop failure, massacres, and disease; the romaniticism that existed once has been irreparably damaged, and that's OK. There's also straight up heavy duty fantasy here for the children, and that might actually be better for them than having to hear about atrocities and starvation. Rapid City is home to Story Book Island, the first of the two storybook parks in the state. There's a carousel, a "train" ride (not on actual tracks, it rides on pavement), and a bunch of fairytale sets to gawk at. Storybook Land (and the expansion Land of Oz) is located in Aberdeen, and it manages to actually have a few rides, including a kiddie coaster. The Great Plains Zoo of Sioux Falls goes with animals as its overarching theme, but has a bonus carousel for those interested in such things.
Family Entertainment Style attractions are also fairly common in the state given the fact that it's South Dakota. Thunder Road Family Fun Park has three locations: the Sioux Falls one possesses a coaster (Wisdom kiddie) matched up with a Tilt A Whirl, Bumper Boats, Go Karts, and mini golf. Karttrax in Yankton has some truly messed up looking Sprint Car go karts that may be homemade (can't tell). Rush Mountain Adventure Park does the Summer Ski Resort stuff like have a Wiegland Mountain Coaster and ziplining. There's two separate maze attractions (Miner's Maze and Black Hills Maze in Rapid City), and even the fairgrounds get into the action.
South Dakota does have several water parks: Wild Water West is the most significant outdoor facility, and has a few modern plastic slides along with a lazy river, go karts, and mini golf. Evans Plunge is an indoor spot that actually draws from a mineral spring (naturally heated to 87") with a few indoor slides and lots of room to swim. WaTiki is a more traditional indoor water park, with 30,000 square feet of space and lots of kid's water play areas.